Derek brings up a good
point, here. What, exactly, makes one a designer? If the show has no formal conceptual production process, does that mean that there is no designer? And what does that mean for shows that are busked live? What constitutes a design?
I think the terminology that you are using is more definitive of the type of "design" you speak of in the first post. If you consider a quality jam session, single musician or an entire band. While those of us who enjoy this type of music (you Dead-heads and Phish fans, especially), I wouldn't consider anyone a composer/song-writer at that moment. They are simply using their talent as a musician, based off previous experience, to provide a great sound. Even if there is a leader to the group guiding the jam session, that person is still not the song-writer.
Now, like the HS student doing their
flash and trash design on an empty
stage, there is still experience being collected. The band leader may use some of the sounds created in the jam session as inspiration for a future song as well as the student taking looks and using them for actual designs later on.
I worked in a roadhouse, similar to The Egg, but on a larger scale (we had the biggest Broadway shows down to small regional acts, speakers such as the Dali Lama and final Presidential debates, and everything in between). There were many times that one of the technical directors would turn to me and say, I need such and such for this show. There is not a
plot, and only a basic description of the show, make it good. I wasn't ever billed as the
lighting designer,
lighting director, or anything since that isn't how the operation worked. If I were to do a website for my designs, I might list one of these as an example of my work, but I wouldn't consider it a "design".
For a design, there is more of a process which has many different elements, which may or may not all be present in the design. As with Derek's list, there are many things to be considered in a design, but they may be applied to many different types of productions/situations. Certainly a rep
plot will affect your design, as does the architecture of a specific
venue, the locations of a
lineset, or many other variables.
But, for what you did, along with many other similar situations, I would go with your term of "
busking". This is what we do for many corporate events,
one-off productions, concerts, and for idiot
road LDs.